A Least Square Finite Element Technique for Transonic Flow with Shock,

Abstract

The governing differential equation for the one-dimensional, transonic flow in a laval nozzle in the vicinity of the throat was obtained in the non-dimensional form. A least square finite element technique was used with a linearly interpolating polynomial to reduce the governing equation to a system of non-linear algebraic equations which were solved numerically by Newton's method. The system of partial differential equations for the two dimensional flow in a laval nozzle was also obtained in the non-dimensional form. The method of integral relations was used to replace the original system of partial differential equations by a system of ordinary differential equations. Using the least square finite element technique a computer program was developed for the construction and solution of the non-linear equations for the laval nozzle problem. The results including the location of the shock in the flow are presented. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 22, 1977
Accession Number
ADA093458

Entities

People

  • Aspi Rustom Wadia

Organizations

  • Sibley School of Mechanical and Aerospace Engineering

Tags

Communities of Interest

  • Air Platforms
  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Acoustic Velocity
  • Agreements
  • Boundaries
  • Computer Programs
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Flow
  • Geometry
  • Laval Nozzles
  • Linear Algebraic Equations
  • Mach Number
  • Nozzles
  • Partial Differential Equations
  • Shock Waves
  • Transonic Flow
  • Two Dimensional

Readers

  • Calculus or Mathematical Analysis
  • Combustion and Flow Dynamics.
  • Fluid Dynamics.